CTET Mathematics Pedagogy part -1

This is the first part of Mathematics Pedagogy.

1. CTET Mthematics Mathematics Pedagogy

2. CTET Mathematics include two important topics, CONTENT and PEDAGOGY. Both topic are of 15 marks each. In this video we will understand Mathematics Pedagogy. At the end of this video we will be able to understand following topics: Nature of Mathematics, Place in Curriculum Problems in teaching Error Analysis Diagnostic & Remedial Teaching Now let’s start our topic, Mathematics Pedagogy.

3. Mathematics Pedagogy First, lets understand both the term separately. What is Pedagogy:- Pedagogy is an art and science (and may be even craft) of Teaching. A good way of exploring pedagogy is as the process of accompanying learners; caring for and about them; and bringing learning into life. What is Mathematics:- Mathematics has no specific Definition. Some define Mathematics as a Science of calculation, some as a Science of Space and Number and some as a Science of Measurement, Magnitude and Direction. The meaning of the world Mathematics is “The Science in which Calculation are Prime”.

4. Nature of Mathematics Nature of Mathematics A Science of Discovery An Intellectual Game The Art of Drawing Conclusion A Tool Subject A System of Logical Processes An Intuitive Method Mathematics relies on both logic and creativity, and it is pursued both for a variety of practical purposes and for its intrinsic interest. For some people, and not only professional mathematicians, the essence of mathematics lies in its beauty and its intellectual challenge. 

5. NCF-2005 Mathematics Guiding Principles of NCF‐2005 • Connecting knowledge to life outside the school. • Ensuring that learning is shifted away from the rote methods. • Enriching the curriculum to provide for overall development of children rather than remain textbook centric. • Making examination more flexible and integrated into classroom life. For Mathematics Vision of school Mathematics has been laid in NCF-2005 as follows: - Children learn to enjoy Mathematics rather than fear it. - Connecting knowledge to life outside the school. - Ensuring that learning is shifted away from the rote methods. - Enriching the curriculum to provide for overall development of children rather than remain textbook centric. - Making examination more flexible and integrated into classroom life. - Children learn important Mathematics: Mathematics is more than formulas and mechanical procedures. ‐ - Children see Mathematics as something to talk about, to communicate through, to discuss among them, to work together on. - Children pose and solve meaningful problems. - Children use abstractions to perceive relation-ships, to see structures, to reason out things, to argue the truth or falsity of statements. - Children understand the basic structure of Mathematics: Arithmetic, Algebra, Geometry and Trigonometry, the basic content areas of school Mathematics, all offer a methodology for abstraction, structuration and generalization. - Teachers engage every child in class with the conviction that everyone can learn Mathematics.

6. Strategies of Teaching Mathematics Strategies of Teaching Math Written Work Oral Work Group Work Homework/ Home Assignment Supervised Study

7. Written Work :- in order to attain precision and accuracy, written work is essential in Mathematics. Oral and written work in mathematics are combined to make the process of instruction complete. Oral Work :- in mathematics, oral work is not only interesting but may be effective especially in the initial stages. An appeal to the eye and ear is more effective than written work. Oral work helps us in mental calculation. It gives a quick and easy start to the process of learning. Group work :- in this teacher teaches by activities, projects, assignments or practical work. Group work is needed to consider, examine and investigate various aspects of a question, topic or problem and for doing homework.

8. Home Assignment/ Homework :- homework in mathematics may consist of some problems based on facts taught in the classroom. Homework should be assessed as a part of internal assessment and proper weightage should be given. Supervised Study :- it introduces the regularity in work and ensures sustained progress. In this technique both the teacher and child remain active. It is the teaching of understanding level. Steps for Supervised Study Introduction/ preparation for their study. Instruction for the study Supervision by the teacher. Development of blackboard summary.

9. Reason for Keeping Mathematics in School Curriculum Mathematics is the basis of all Science The different branches of science likewise Physics, Chemistry, Astronomy, Biology, Medical Science, Geology, Astrology etc are the important subjects which are based on mathematics, e.g., area, volume, weight, density, number of atom and electrons, medicines all are related to mathematical study. Mathematics is Related to Human Life Right from getting up in morning till going to bed, we need the help of mathematics. Even our body and organs are connected to mathematics. For planning, purchasing, each and every aspect involves the use mathematics.

10. Mathematics Generates Logical Attitude In order to solve a mathematical problem, a child has to think logically. Every step is related to other step on the basis of some logic with which child develops his mental abilities and it further effects his intellectual development. Mathematics Provide a Definite Way of Thinking The children who study mathematics develop their attitude with which they learn to work systematically, regularly and properly. Along with this, it also develops a logical thinking in them. Mathematics is an Exact Science Mathematical sciences is a group of areas of study that includes, in addition to mathematics, those academic disciplines that are primarily mathematical in nature but may not be universally considered subfields of mathematics proper. Statistics,  for example, is mathematical in its methods but grew out of scientific observations which merged with inverse probability.

11. Language of Mathematics The  language of mathematics  is the system used by  mathematicians to communicate mathematical ideas among themselves. This language consists of a substrate of some natural language (for example English) using technical terms and grammatical conventions that are peculiar to mathematical discourse, supplemented by a highly specialized symbolic notation for mathematical formulas. Like any language, it is made up of Concepts, Terminology, Symbols, Algorithms and Syntax which is peculiar to it. Mathematics as a Language Mathematics is itself a language with its own symbols, words and rules of syntax. It is based on a certain consistent set of assumption and built up from there according to the rules of logic.

12. Community Mathematics The subject of Mathematics can be understood in an efficient way through the communication in the community of teachers and student. A particular class are divided into a number of small group and then allowed to create different solutions to a lesson problem and after that present their solutions to their classmates. Thus, by choosing Mathematics tasks and problems evoking significant Mathematics and prompts students to discuss their mathematical thinking, the student’s mathematical communication can be established . Mathematical Communication Mathematical Communication is a developing collection of resources for engaging students in writing and speaking about mathematics, whether for the purpose of learning mathematics or of learning to communicate as mathematicians.

13. Mathematical communication is similar to all other forms of communication – the aim is to effectively convey an idea.  Ask yourself: what is the basic message you want to send?  Aspire to share these mathematical ideas in a way that instils understanding, engagement and curiosity within your audience . Mathematical communication is a two-way process Audience participation and feedback is desirable and should be encouraged. This enables the audience to contribute to – and to view themselves as part of – the communication process . Communication is an essential piece in the learning process – it provides students an opportunity to justify their reasoning or formulate a question, leading to gained insights about their thinking. In order to communicate their thinking to others, students must be given authentic tasks to reflect on. Through cooperative learning, students can learn from the perspectives and mathematical processes of others. Further, they can learn to evaluate the thinking of others, building on those ideas for their own assessment.